The past two decades have witnessed a booming development of theories and applications of quantum systems. The discipline of quantum signal processing (QSP) [1]} was founded under the construction of quantum mechanics frameworks [2]} and studies the manipulation, detection and restoration of quantum signals.
One important branch of study of quantum systems is the detection and discrimination of states. In quantum signal processing, detecting the quantum state with good accuracy lays a foundation for many signal processing problems including the reconstruction of the original quantum state.
